Cataclysm was an expansion in name only. Whether we call the remade zones new content or not, they replace the old Azeroth, which means that they do not expand the world, merely change it (a lot). We did get a few entirely new zones for 80+, but in terms of quests, levels, and geography, the remade world was the big thing.
This caused some problems. Rohan pointed out a big one: the remade zones don't make a whole lot of sense to a new player. This may be a selective perception, but I felt like vanilla, and then eventually LK, did a good job of introducing the story, so that even without needing to play earlier Warcraft games or reading books, it all made some amount of sense. BC was a bit more disorienting, but some of that may have been merely the sudden influx of glowing purple crystals. But the remade Azeroth feels as if it's a huge reference to the old Azeroth, which is of course, gone.
This creates a worst of both worlds scenario. New players may wonder what the world was before, and have no good way to find out, since that content is all gone. As Rohan describes it, it's like if volume IV of a series came out, but they burned volume I. It's not much better for veterans who may miss the old content. Or even worse, since not everything is completely new, we can see what is new and what is old. The old feels lazy, or in the case of some tweaked quest chains (I'm looking at you, Darrowshire), butchered. Meanwhile new content can feel out of place in this almost the old place but not quite.
Then there's the time problem. Before WoW followed something almost like linear time: Kalimdor and Eastern Kingdoms (pre-60) came first, then Outland came next (60+), and finally Northrend (70+). Levels fit the timeline. There was the ability to go back to old zones or do them out of order, but that was a player action; the structure of the world made sense. The remake breaks that, with the 1-60 content taking place after the 60-80 content.
Cataclysm as a proper expansion would have fixed this, along with other problems. As an expansion the remade Azeroth would have come after Northrend, somewhere in the 80+ range. How exactly this would fit in, I'm not sure, but the simplest way seems to be a Caverns of Time portal that can switch us between new and old Azeroth, much as the Dark Portal moves us between Azeroth and Northrend.
Having only five more levels made the new content feel lacking, if only because people like more numbers, regardless of the actual content. But if the remade Azeroth started at 80, it could have easily added another five levels. At the least, it would have allowed the devs to speed up Uldum and Vash'jir, both of which dragged on a bit, despite having cool concepts.
In terms of story-telling, it would make the expansion more potent for new players. Sure, the scale is obvious, but it's all something that happened to someone else. Pre-Cataclysm players would instead know what used to be, remember questing there, have some attachment, good or bad, to what was destroyed, which gives the destruction that much more impact.
Compare this with the Caverns of Time instances, which do this, but in reverse, showing us what our world used to be, which can still draw on memory and attachment to give a greater sense of meaning. Players in the Culling of Stratholme can see the city before it is burning, filled with people, in its full splendor, all of which would be meaningless if they didn't yet know it as a burning city of the dead. Similarly, though in my experience, less strongly, the Escape from Durnhold let us see it before the Syndicate, and before Thrall blew it up with lightning (something which I don't think WoW mentions). It adds a little bit more meaning to the rotten state of Tarren Mill to see it before the Forsaken moved in, before it was decaying.
In short form: Cataclysm is more powerful if it is preceded by vanilla.
But remaking Azeroth, duplicating it for a single expansion, does have problems.
Right now leveling is too fast, despite using less than the full world for an entire 60 levels. The speed of all the new and remade zones compressed into only 10 levels would be terrible. We'd get a quarter of a level before leaving a zone, meaning either extremely short zones (few quests and done quickly) or unbearably slow leveling. Yes, even I, the advocate of slow leveling, do believe it can be too slow. This could be fixed up a bit by adding levels. With 20 levels I think a new Azeroth could be made to work as an expansion. However Blizzard would have to throw out their philosophy of maintaining a constant time to max level with each expansion (which I think they should do anyway).
Two Azeroths could feel repetitive, despite the separation of two expansions between them. This would only get worse with alts. Creating entirely fresh quests would help, but that would further increase the development work needed.
Instances would have been a huge problem, especially if heroics were mixed in. I have no good ideas for dealing with those.
Perhaps the solution would have been two Cataclysms, meaning to expansions, one after LK and another one after that. One expansion for Kalimdor (Horde bias!), using that continent remade for ten levels and the raids to go with. Then something triggers the same for the Eastern Kingdoms, for another ten levels. This would be more than a little bit contrived, but let's face it, "dragon who slept all the time suddenly wakes up right as we're looking for an excuse to add flying mounts to even more areas" isn't exactly a logical progression. Well okay, dev/marketing logic, but not normal person logic.
Now if only I had a time machine and a printout of the sub numbers for cata...